where \(\mathbf {D}=\operatorname{diag}\lbrace d_1,\ldots ,d_n\rbrace \) , the diagonal matrix of the out-degrees of the vertices and \(\mathbf {W}\)  the weighted adjacency matrix. For any graph signal \(f\) , measure \(\mu :\mathcal {V}\mapsto [0,\infty )\)  and states \(x,y \in \mathcal {V}\) , we adopt the following conventions [1]}:
\(\mathbf {P}f(x)&=\sum _{y\in \mathcal {V}}p(x,y)f(y),\\\mu \mathbf {P}(y)&=\sum _{x\in \mathcal {V}}\mu (x)p(x,y).\) 
